Shannon sampling II: Connections to learning theory

By Steve Smale, Ding-Xuan Zhou. 2005

239 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Signal Processing

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Citations in the corpus

On regularization algorithms in learning theory (2007, background): “For this kind of prior (but Hölder source condition) the best results were obtained in Smale and Zhou (2005a) for Tikhonov regularization.”
Regularized least square regression with dependent samples (2010, methodology): “As for fγ , we have the representation [ 13 ]”
Geometry on Probability Spaces (2009, background): “In vision it would be useful to do analysis on the space of images and an image is a function on a patch.”
Spectral Algorithms for Supervised Learning (2008, background): “been recently proposed in ( Smale & Zhou, 2004, 2005b ) whereas (De Vito,”
Vector valued reproducing kernel Hilbert spaces and universality (2008, methodology): “In learning theory, reproducing kernel Hilbert spaces (RKHS) are an important tool for designing learning algorithms, see for example [8, 29 , 31] and the book [9].”
Sampling in paley-wiener spaces on combinatorial graphs (2008, background): “Combinatorial graph, combinatorial Laplace operator, discrete Paley- Wiener spaces, Shannon sampling, discrete Plancherel-Polya and Poincare inequalities. c©2008 American Mathematical Society Reverts to public domain 28 years from publication 5603 sequence of points {xj} and still have a stable reco”
Gradient-Based Kernel Dimension Reduction for Regression (2014, background): “These facts have been proved in various contexts (e.g. Smale and Zhou, 2005, 2007, Caponnetto and De Vito, 2007, Bauer et al., 2007), so the proof is omitted.”
A note on application of integral operator in learning theory (2009, methodology): “[13,16]).”
DISCRETIZATION ERROR ANALYSIS FOR TIKHONOV REGULARIZATION (2006, background): “Analysis and Applications, Vol. 4, No. 1 (2006) 81–99 c© World Scientific Publishing Company”
Learning from Examples as an Inverse Problem (2005, unknown): “Some result in this direction can be found in Steinwart (2004) for classification setting.”
Application of integral operator for regularized least-square regression (2009, methodology): “∗Corresponding author Keywords: regularized least square regression, integral operator, reproducing kernel Hilbert space, consistency.”
Learning Theory Estimates via Integral Operators and Their Approximations (2007, background): “The rates for this approximation in L 2 ρ X have been considered in [3] [4] [16] [11] [14], while the approximation in the space H K (hence in L ∞ ρ X by (1.2) and in C s by [17]) has been shown in [11].”